Persistence Partial Matchings Induced by Morphisms between Persistence Modules

07/09/2021

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by   R. Gonzalez-Diaz, et al.

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The notion of persistence partial matching, as a generalization of partial matchings between persistence modules, is introduced. We study how to obtain a persistence partial matching 𝒢_f, and a partial matching ℳ_f, induced by a morphism f between persistence modules, both being linear with respect to direct sums of morphisms. Some of their properties are also provided, including their stability after a perturbation of the morphism f, and their relationship with other induced partial matchings already defined in TDA.